An iterative estimation method and device for a composite cascading failure propagation influence range

Abstract

The application relates to the technical field of smart grids, in particular to a method and device for iteratively estimating the influence range of a composite cascading fault propagation, which can optimize resource allocation, strengthen the protection and monitoring of key nodes, take preventive and control measures before the large-scale propagation of faults, and reduce the influence of power outages on the economy and society. The method comprises the following steps: abstracting the interaction relationship of nodes in a smart grid as G=(G p , G c , E c→p , E p→c ); wherein G p (P, E p ) is a physical network, P is a physical node set, G c (C, E c ) is an information network, and C is an information node set; based on the network state information at the current moment, the state transition probability of each node is calculated by decoupling the time and space dependence; the probability distribution of the state of each node in the next time slice and the average number of nodes affected in the entire network are iteratively obtained according to the state transition probability of each node, and the estimation result of the influence range of the composite cascading fault propagation is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of smart grid, in particular to an iteration estimation method and device for influence range of composite cascading fault propagation. BACKGROUND

[0002] The smart grid couples the physical network for providing power with the information network for providing control function, thereby greatly improving the reliability of the power grid. The information network can intelligently monitor and control the power grid, optimize the operation and management of the power grid, help reduce the construction and operation cost of the power grid, and improve the economic benefit and resource utilization efficiency of the power grid. However, the high dependence relationship between nodes also makes the smart grid more sensitive to faults. A fault in a few nodes can be propagated in a large range, that is, a cascading fault is formed.

[0003] The existing method can analyze the propagation of a single fault type, but it is difficult to analyze the composite cascading fault of the fault propagation in the physical network and the information network. In recent years, network security incidents have gradually increased, and the information network is becoming an attack entry for the power grid. The composite cascading fault is likely to become the main fault type in the future. Estimating the propagation range of the cascading fault helps the power grid operator better understand the weak links of the power grid.

[0004] Therefore, it is urgent to provide a new estimation method to optimize resource allocation, strengthen protection and monitoring of key nodes, take preventive and control measures before large-scale propagation of faults, and reduce the impact of power outages on the economy and society. SUMMARY

[0005] In order to solve the problem of how to optimize resource allocation, strengthen protection and monitoring of key nodes, take preventive and control measures before large-scale propagation of faults, and reduce the impact of power outages on the economy and society, the present application provides an iteration estimation method and device for influence range of composite cascading fault propagation.

[0006] Embodiments of the present application are implemented as follows:

[0007] In a first aspect, the present application provides an iteration estimation method and device for influence range of composite cascading fault propagation, comprising:

[0008] The interaction relationship of nodes in the smart grid is abstracted as G=(G p , G c , E c→p , E p→c );

[0009] G p (P, E p ) is a physical network, P is a set of physical nodes, G c (C, Ec ) is the information network, c is the set of information nodes;

[0010] Based on the network state information at the current time, the state transition probability of each node is calculated by decoupling the time and space dependence, using the Markov property;

[0011] According to the state transition probability of each node, the probability distribution of the state of each node in the next time slice and the average number of nodes affected in the entire network are obtained iteratively, and the estimation result of the influence range of the compound cascading failure propagation is obtained.

[0012] In a possible implementation, the initial state of the network state information is recorded as t = 0, and and are called the initial snapshot of the system.

[0013] In a possible implementation, given the initial snapshot, the state transition of the system can be given by the following time recursive master equation:

[0014]

[0015]

[0016] At any time t, the estimated number of power grid physical nodes that can still work normally is

[0017]

[0018] In a possible implementation, the propagation process of the compound cascading failure adopts an asynchronous iterative decoupling manner, that is, the failure propagation in the information network and the physical network alternately proceeds in each time step.

[0019] In a possible implementation, in the calculation of the information network, the propagation in one time step is divided into two stages, that is, the time

[0020] In a possible implementation, the state correlation between adjacent nodes is considered, and the neighbor state Node c i The neighborhood infection probability in a time slice And the probability that the neighborhood is in the giant connected component

[0021] Wherein, is the average probability that any node is not in the giant connected component, q k，t-1 is the excess distribution; in the transition probability, the time dependence is contained in I i (t) and LCC i(t) among them, while the spatial dependence is captured by the joint conditional probabilities Description.

[0022] In one possible implementation, the decomposition is based on conditional probabilities, with the help of intermediate variables and The state transition probabilities are written as follows:

[0023] Node c i In The probability of losing all power (transition to offline state) is:

[0024]

[0025] Node c i In The probability of remaining in normal state (susceptible state) is:

[0026]

[0027] Node c i In The probability of being infected (transition from susceptible state to infected state) is:

[0028]

[0029] Node c i In The probability of not being in the giant connected component (transition to offline state) is:

[0030]

[0031] In one possible implementation, in the calculation of the physical network, similar to the calculation in the information network, the neighborhood states are enumerated using the total probability formula to derive:

[0032] Physical node p i The probability of not losing control (i.e., the information node on which this node depends is still in the susceptible state) is:

[0033]

[0034] Physical node p i The probability of not being overloaded (i.e., the current load is less than or equal to the maximum threshold) is:

[0035]

[0036] In one possible implementation, the load of a physical node p i is the load it originally has plus the load transferred through load balancing after the failure of its neighbors, i.e.,

[0037]

[0038] The load assigned to the neighbors by the physical node when changing from the normal state to the failure state is calculated by the following formula:

[0039]

[0040] In a second aspect, the application provides an iterative estimation device for the influence range of a composite cascading failure propagation, comprising:

[0041] A network input module is configured to abstract the interaction relationship of nodes in a smart grid as G=(G p , G c , E c→p , E p→c );

[0042] A probability calculation module is configured to calculate the state transition probability of each node based on the network state information at the current time by decoupling the time and space dependence relationship and using the Markov property.

[0043] An iterative estimation module is configured to iteratively obtain the probability distribution of the state of each node in the next time slice and the average number of affected nodes in the entire network based on the state transition probability of each node, and obtain the estimation result of the influence range of the composite cascading failure propagation.

[0044] The technical scheme provided by the application can achieve at least the following beneficial effects:

[0045] The iterative estimation method for the influence range of the composite cascading failure propagation provided by the application,

[0046] By considering the smart grid topology information in the form of an adjacency matrix, the precision loss caused by the estimation based on the state mean value is avoided, the result is closer to the true value, and the method has universality.

[0047] By decoupling the spatial factors (i.e., the communication relationship between nodes in the information network and the load balancing relationship between nodes in the physical network) and the time factors (i.e., the load balancing and virus propagation have a sequence) relied on by the composite cascading failure propagation through the method of probability analysis, the dynamic process has local Markov property, so that the development process can be deduced.

[0048] By simultaneously solving the mutual influence between the nodes in the information network by adding the edge distribution term, the precision loss caused by the assumption of independent node state in the traditional estimation is avoided.

[0049] By constructing the iterative deduction algorithm, given any initial state and network topology information, the expected influence range of the composite cascading failure at any time and the failure probability of each node in the network can be output by iterative deduction. BRIEF DESCRIPTION OF DRAWINGS

[0050] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced. Obviously, the drawings described below are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0051] Figure 1 is a flowchart of an iterative estimation method of the influence range of the composite cascading failure propagation according to an example embodiment of the present application;

[0052] Figure 2 is a flowchart of an iterative estimation algorithm of the influence range of information propagation according to an example embodiment of the present application;

[0053] Figure 3 is a structural schematic diagram of an iterative estimation device of the influence range of the composite cascading failure propagation according to an example embodiment of the present application;

[0054] Figure 4 is a schematic diagram of the composite cascading failure propagation process in the smart grid according to an example embodiment of the present application.

[0055] Reference Signs:

[0056] 1, network input module; 2, probability calculation module; 3, iterative estimation module. DETAILED DESCRIPTION

[0057] In order to make the purposes, embodiments and advantages of the present application more clear, the example embodiments of the present application will be described clearly and completely below with reference to the drawings of the example embodiments of the present application. Obviously, the described example embodiments are only some embodiments of the present application, not all embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not intended to limit the present application.

[0058] It should be noted that the brief description of the terms in the present application is only for the convenience of understanding the following described embodiments, and is not intended to limit the embodiments of the present application. Unless otherwise specified, these terms should be understood according to their ordinary and general meanings.

[0059] The terms "first", "second", "third", etc. in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar or identical objects or entities, and do not necessarily mean to limit the specific order or sequence, unless otherwise specified. It should be understood that the terms used in this way can be interchanged under appropriate circumstances.

[0060] The terms "include" and "have" and any variations thereof are intended to cover but not exclusive inclusion, for example, a product or device including a series of components does not have to be limited to all components listed clearly, but can include other components not listed clearly or inherent to these products or devices.

[0061] Before explaining the iterative estimation method of the propagation influence range of the composite cascading failure provided by the embodiments of the present application, the application scenarios and implementation environments of the embodiments of the present application are introduced.

[0062] The smart grid couples the physical network of power supply with the information network of control function, thereby greatly improving the reliability of the power grid. The information network can intelligently monitor and control the power grid, optimize the operation and management of the power grid, help reduce the construction and operation cost of the power grid, and improve the economic benefit and resource utilization efficiency of the power grid. However, the high dependence relationship between nodes also makes the smart grid more sensitive to failure, and a failure of a few nodes may be widely propagated, that is, a cascading failure is formed.

[0063] The existing method can analyze the propagation of a single failure type, but it is difficult to analyze the composite cascading failure of the failure propagation in the physical network and the information network. In recent years, network security incidents have gradually increased, and the information network is becoming an attack entry for the power grid. The composite cascading failure is likely to become the main failure type in the future, and the estimation of the propagation range of the cascading failure helps the power grid operator to better understand the weak links of the power grid.

[0064] Therefore, it is urgent to provide a new estimation method to optimize resource allocation, strengthen protection and monitoring of key nodes, take preventive and control measures before large-scale propagation of failure occurs, and reduce the impact of power outage accidents on the economy and society.

[0065] Based on this, the application provides an iterative estimation method and device for the influence range of composite cascading fault propagation. First, a management mechanism describes the topology of a smart grid as an adjacency matrix with dimensions (the smart grid is modeled as a coupling of a physical network and an information network, and the number of nodes in the physical network and the information network is ). Then, the propagation strength of a virus in the information network and the current influence range are obtained through short-time observation at the initial stage of propagation. On this basis, the spatial and temporal factors on which the fault propagation depends are decoupled based on the local Markov property of the fault propagation process, and the influence range of the power grid physical fault at any time under the condition of simultaneous propagation with the corresponding information network infection is calculated based on a recursive expression.

[0066] Next, the technical solutions of the application and how the technical solutions solve the above technical problems will be described in detail through embodiments and in combination with the drawings. The embodiments can be combined with each other, and the same or similar concepts or processes can not be described again in some embodiments. Obviously, the described embodiments are part of the embodiments of the application, not all.

[0067] Figure 1 FIG. 1 is a flowchart of an iterative estimation method for the influence range of composite cascading fault propagation according to an example embodiment of the application.

[0068] In an example embodiment, as shown in FIG. 2, an iterative estimation method for the influence range of composite cascading fault propagation is provided, which can include the following steps in the embodiment: Figure 1

[0069] Step 100: Abstract the interaction relationship of nodes in a smart grid as G=(G p , G c , E c→p , E p→c ).

[0070] Wherein, G p (P, E p ) is a physical network, P is a physical node set, G c (C, E c ) is an information network, and C is an information node set.

[0071] Step 200: Based on the network state information at the current time, the state transition probability of each node is calculated by decoupling the time and space dependence and using the Markov property.

[0072] Step 300: According to the state transition probability of each node, the probability distribution of the state of each node in the next time slice and the average number of affected nodes in the entire network are iteratively obtained, and the estimation result of the influence range of composite cascading fault propagation is obtained.​

[0073] In a possible implementation, the estimation method firstly abstracts the interaction relationship of nodes in the smart grid into a graph G=(G p , G c , E c→p , E p→c ), wherein G p (P, E p ) is a physical network, P is a physical node set, G c (C, E c ) is an information network, and C is an information node set.

[0074] Then, based on the network state information (referred to as a network snapshot) at the current time, the state transition probability of each node is calculated by decoupling the time and space dependence, and the probability distribution of the state of each node in the next time slice and the average number of nodes affected in the entire network are iteratively obtained, so that the influence range of the compound cascading failure propagation is estimated.

[0075] In a possible implementation, the specific implementation is as follows:

[0076] The influence range of the compound cascading failure propagation is defined as:

[0077] Without loss of generality, the time when the initial state of the observed network is observed is recorded as t=0, and the initial state of the system is recorded as referred to as the initial snapshot of the system.

[0078] Given the initial snapshot, the state transition of the system can be given by the following time recursive master equation:

[0079]

[0080]

[0081] At any time t, the estimated number of physical nodes in the power grid that can still work normally is:

[0082]

[0083] Iterative calculation of transition probability and influence range

[0084] The propagation process of the compound cascading failure is decoupled in an asynchronous iteration manner, that is, the failure propagation in the information network and the physical network is alternately performed in each time step.

[0085] Firstly, the calculation in the information network, the propagation in one time step is divided into two stages, that is, the time Considering the state correlation between adjacent nodes, we enumerate the states of their neighbors using the law of total probability. Node c i Probability of infection in a neighborhood within a time slice And the probability that the neighborhood is in a maximally connected component.

[0086] in:

[0087] q is the average probability that any node is not in a maximally connected component. k，t-1 It is an excess degree distribution.

[0088] In the transition probability, time dependence is included in I. i (t) and LCC i In (t), spatial dependence is determined by joint conditional probability. Description. To avoid prediction accuracy bias caused by the assumption of independent node states in traditional methods, this invention decomposes the data based on conditional probability and utilizes intermediate variables. as well as The one-step state transition probability can be written in the following form:

[0089] That is, node c i exist The probability of losing all power (transferring to an offline state) is:

[0090]

[0091] Node c i exist The probability of maintaining a normal state (susceptible state) is:

[0092]

[0093] Node c i exist The probability of being infected (transforming from a susceptible state to an infected state) is:

[0094]

[0095] Node c i exist The probability that the component is not in a maximally connected component (transitioning to an offline state) is:

[0096]

[0097] Equations (5), (6), and (7) are sufficient to fully describe the state changes of a node during the simultaneous propagation of positive and negative information.

[0098] The above formula shows that, given an initial state, the dynamic process of virus transmission is dependent in both time and space, i.e., node c i status It depends on one's state in the previous time segment. The state of neighboring nodes (within the space) And the propagation actions of neighboring nodes within the current time slice (infecting or not in a maximally connected component). The propagation action is determined by the transition probability within each time slice t. The description is as follows, where s and r ∈ {0, 1, -1}:

[0099]

[0100] in, This indicates that at a fixed node c j After node c is in state w i The probability of a state transitioning from u to v within time slice t is calculated as follows:

[0101]

[0102] The next step involves computation in the physical network, which follows a similar approach to computation in the information network. The derivation is performed by enumerating the neighborhood states using the law of total probability.

[0103] physical node p i The probability that the node has not lost control (i.e., the information nodes it depends on are still in a vulnerable state) is

[0104]

[0105] physical node p i The probability of not being overloaded (i.e., the current load is less than or equal to the maximum threshold) is:

[0106]

[0107] And a physical node p i The load is its original load plus the load transferred through load balancing after a neighbor failure, i.e.

[0108]

[0109] The load allocated to neighbors by a physical node when it transitions from a normal state to a fault state is calculated by the following formula:

[0110]

[0111] Last updated degree distribution of the information network:

[0112]

[0113] wherein,

[0114] To solve the real-time influence range of the compound cascading failure, the following six transition probability matrices are defined as intermediate variables:

[0115]

[0116] Figure 2 is the flowchart of the iterative estimation algorithm of the information propagation influence range shown in an exemplary embodiment of the present application.

[0117] Based on the above definitions, an iterative estimation algorithm is proposed, which can be used for the smart grid G=(G p , G c , E c→p , E p→c ) with any topology, and any initial network snapshot The influence range of the compound cascading failure on the network G=(G e , G e , E p , E c ) at any time t c→p (t p→c >0) is iteratively estimated, and the specific implementation process of the iterative algorithm is shown in Figure 2 .

[0118] In the above iterative estimation method of the propagation influence range of the compound cascading failure, the smart grid topology information is considered in the form of an adjacency matrix, which avoids the precision loss caused by the estimation based on the state mean, makes the result closer to the true value, and makes the method have universality.

[0119] By decoupling the spatial factors (i.e. the communication relationship between nodes in the information network, the load balancing relationship between nodes in the physical network) and the time factors (i.e. load balancing, virus propagation has a sequence) relied on by the propagation of the compound cascading failure through the method of probability analysis, the dynamic process has local Markov property, so that the development process can be deduced.

[0120] By simultaneously adding edge distribution items to the mutual influence between nodes in the information network, the precision loss caused by the assumption of independent node states in the traditional estimation is avoided.

[0121] By constructing an iterative deduction algorithm, given any initial state and network topology information, the expected influence range of the compound cascading failure in the network at any time and the failure probability of each node can be output by iterative deduction.

[0122] It should be understood that although the steps in the flowcharts involved in the above embodiments are shown in sequence as indicated, these steps are not necessarily executed in the order as indicated. Unless explicitly stated herein, the execution of these steps is not strictly limited in sequence, and these steps can be executed in other orders. Moreover, at least some of the steps in the flowcharts involved in the above embodiments can include multiple steps or multiple stages, which are not necessarily executed at the same time but can be executed at different times, and the execution of these steps or stages is not necessarily sequential but can be executed in rotation or alternation with at least some of the other steps or the steps or stages in the other steps.

[0123] Corresponding to the above embodiments of the method for iteratively estimating the impact range of the composite cascading failure propagation, the same technical concept is adopted, and the present application further provides embodiments of a device for iteratively estimating the impact range of the composite cascading failure propagation.

[0124] Figure 3 is a structural schematic diagram of a device for iteratively estimating the impact range of the composite cascading failure propagation according to an exemplary embodiment of the present application.

[0125] In an exemplary embodiment, as shown in Figure 3 , the device for iteratively estimating the impact range of the composite cascading failure propagation comprises:

[0126] a network input module 1 configured to abstract the interaction relationship of the nodes in the smart grid as G=(G p , G c , E c→p , E p→c );

[0127] a probability calculation module 2 configured to calculate the state transition probability of each node by decoupling the time and space dependence relationship and using the Markov property based on the network state information at the current time;

[0128] an iterative estimation module 3 configured to iteratively obtain the probability distribution of the state of each node and the average number of affected nodes in the entire network in the next time slice according to the state transition probability of each node, and obtain the estimation result of the impact range of the composite cascading failure propagation

[0129] Specific limitations regarding the iterative estimation device for the propagation range of complex cascading faults can be found in the limitations of the iterative estimation method for the propagation range of complex cascading faults described above, and will not be repeated here. Each module in the aforementioned iterative estimation device for the propagation range of complex cascading faults can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0130] It can be seen that:

[0131] The estimation in this application offers high real-time performance: traditional estimation methods rely on steady-state analysis and can only estimate the final state of the smart grid system after fault propagation ends, lacking an understanding of the fault propagation process. The algorithm proposed in this invention, through iterative deduction, can estimate the state of the smart grid system at any given time and the fault probability of each node at any given time.

[0132] The estimation accuracy of this application is high: the algorithm proposed in this invention uses the influence of conditional probability and marginal probability distribution on the entire propagation process for estimation, rather than using expectation, which improves the accuracy of the estimation.

[0133] The algorithm in this application has a wide range of applications: in terms of applicable networks, due to the introduction of network topology, the algorithm is applicable to various heterogeneous scenarios with different topologies and parameters; in terms of algorithm execution, the low space and time complexity makes the algorithm suitable for deployment on multiple computing platforms.

[0134] Figure 4 This is a schematic diagram illustrating the propagation process of a complex cascaded fault in a smart grid, as shown in an exemplary embodiment of this application.

[0135] To verify this application, a preliminary experiment was conducted, demonstrating the propagation of complex cascading faults in its smart grid, as follows: Figure 4 As shown, physical nodes may lose control of information nodes or become overloaded, while information nodes may lose power to physical nodes, become infected, or be separated from the maximum connectivity component. Faults caused by multiple reasons propagate simultaneously on the network, causing the node state to change over time.

[0136] Assume the time when the area of ​​influence to be estimated is t. e =1, such as Figure 2 As shown. Figure 2 The smart grid G(G) shown has n=6 p G c E c→p E p→c) is taken as an example, the physical node set is P(p1, p2, p3, p4, p5, p6), the information node set is C={c1, c2, c3, c4, c5, c6}, and it is assumed to be an unweighted graph. Initial network snapshot According to the initial network snapshot and the node load attribute, the iteration method is used to calculate t e =1, the edge distribution of the physical node state Finally, E(|N(t=1)|)=3 is obtained. For t e >1, multiple iterations can be performed according to the algorithm.

[0137] The technical features of the above embodiments can be combined in any manner. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described, but as long as the combinations of the technical features do not contradict, they should be considered as falling within the scope of the present disclosure.

[0138] The above embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be pointed out that for those skilled in the art, some modifications and improvements can be made without departing from the concept of the present application, and these all fall within the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. An iterative estimation method of the propagation influence range of a composite cascade fault, characterized in that, Comprise: The interaction relationship of nodes in a smart grid is abstracted as ; wherein, is a physical network, is a set of physical nodes, is an information network, is a set of information nodes; Based on the network state information of the current time, the state transition probability of each node is calculated by decoupling the time and space dependence and using the Markov property; According to the state transition probability of each node, the probability distribution of the state of each node in the next time slice and the average number of nodes affected in the whole network are obtained iteratively, and the estimation result of the influence range of the composite cascading failure propagation is obtained; The propagation process of the composite cascading failure adopts an asynchronous iteration method, that is, the failure propagation in the information network and the physical network alternately proceeds in each time step; In the computation of information networks, the propagation within one time step is divided into two phases, namely time ; Considering the state correlation between adjacent nodes, the neighbor state is enumerated by using the total probability formula , node The neighborhood infection probability in a time slice And the probability that the neighborhood is in the giant connected component ; where is the average probability that a randomly chosen node is not in the giant connected component, is the excess degree distribution; in the transition probability, the time dependence is contained in and the spatial dependence is described by the joint conditional probability .

2. The method of claim 1, wherein, The time instant of the initial state of the network state information is denoted by and the and are called the initial snapshot of the system.

3. The method of claim 2, wherein the method further comprises: Given the initial screenshot, the state transition of the system is given by the following time recursion main equation: ； ； ； ； ； ； At any moment, the estimated number of grid physical nodes that are still able to work properly is .

4. The method of claim 1, wherein, Decomposition based on conditional probabilities, with the help of intermediate variables and Write the state transition probabilities as follows: Node In The probability of losing all power supply (transition to offline) is: ； Node In The probability of remaining in the normal state (susceptible state) is: ； Node In The probability of being infected (transitioning from susceptible to infected) is: ； Node In The probability of not being in a giant connected component (transition to offline) is: 。 5. The method of claim 1, wherein, In the calculation of the physical network, similar to the calculation in the information network, the neighborhood state is enumerated and deduced by using the total probability formula; Physical node The probability of not losing control (i.e. the information node on which the node depends is still in a susceptible state) is: ； Physical node The probability that a node is not overloaded (i.e. current load is less than or equal to the maximum threshold) is: 。 6. The method of claim 5, wherein the method further comprises: One physical node The load of a physical node is the load it originally has plus the load transferred through load balancing after the failure of its neighbors, i.e. ； ； The load allocated to the neighbor when the physical node is changed from the normal state to the failure state is calculated by the following formula: 。 7. An apparatus for iteratively estimating the impact range of a compound cascading failure, the apparatus being configured to implement the method for iteratively estimating the impact range of a compound cascading failure according to any one of claims 1 to 6, characterized in that, Comprise: a network input module, configured to abstract the interaction relationship of nodes in a smart grid into ; A probability calculation module is configured to calculate the state transition probability of each node by decoupling the time and space dependence and using the Markov property based on the network state information of the current time; An iterative estimation module is configured to obtain the probability distribution of the state of each node in the next time slice and the average number of nodes affected in the whole network according to the state transition probability of each node, and obtain the estimation result of the influence range of the composite cascading failure propagation.

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